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Step-1

Title: Median of triangle

Grade: 7-a Lesson: S3-L2

Explanation:

Step	Type	Explanation	Answer
1	Problem	If AD id the median of triangle ABC and sides AB = 5, BC = 6 and CA = 7, then find the medain AD $1$
2	Given	In a triangle ABC, BD is the median, and sides AB = 5, BC = 6, AC = 7.
3	Formula:	The median of the triangle is given by	\$ BD = \sqrt{\frac{2(AC) ^2 + 2(AB) ^2 - (BC) ^2}{4}} \$
4	Step	Substitute the values.	\$\Rightarrow BD = \sqrt{\frac{2(6) ^2 + 2(5) ^2 - (7) ^2}{4}} \$
5	Step	Calculate the exponents.	\$\Rightarrow BD = \sqrt{\frac{2(36) + 2(25) - 49}{4}} \$
6	Step	Multiply.	\$\Rightarrow BD = \sqrt{\frac{72 + 50 - 49}{4}} \$
7	Step	Add and subtract.	\$\Rightarrow BD = \sqrt{\frac{73}{4}} \$
8	Step	Simplify.	\$\Rightarrow BD = \frac{\sqrt{73}}{2} \$
9	Step	Answer	The value of the median BD of triangle ABC = \$\frac{\sqrt{73}}{2}\$.

Step

Type

Explanation

Answer

Problem

If AD id the median of triangle ABC and sides AB = 5, BC = 6 and CA = 7, then find the medain AD

$1$

Given

In a triangle ABC, BD is the median, and sides AB = 5, BC = 6, AC = 7.

Formula:

The median of the triangle is given by

\$ BD = \sqrt{\frac{2(AC) ^2 + 2(AB) ^2 - (BC) ^2}{4}} \$

Step

Substitute the values.

\$\Rightarrow BD = \sqrt{\frac{2(6) ^2 + 2(5) ^2 - (7) ^2}{4}} \$

Step

Calculate the exponents.

\$\Rightarrow BD = \sqrt{\frac{2(36) + 2(25) - 49}{4}} \$

Step

Multiply.

\$\Rightarrow BD = \sqrt{\frac{72 + 50 - 49}{4}} \$

Step

Add and subtract.

\$\Rightarrow BD = \sqrt{\frac{73}{4}} \$

Step

Simplify.

\$\Rightarrow BD = \frac{\sqrt{73}}{2} \$

Step

Answer

The value of the median BD of triangle ABC = \$\frac{\sqrt{73}}{2}\$.